{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T22:12:47Z","timestamp":1782943967953,"version":"3.54.5"},"reference-count":37,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,19]],"date-time":"2021-10-19T00:00:00Z","timestamp":1634601600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Nature Science Foundation of China","award":["61673079"],"award-info":[{"award-number":["61673079"]}]},{"DOI":"10.13039\/501100005230","name":"Natural Science Foundation of Chongqing","doi-asserted-by":"publisher","award":["cstc2018jcyjAX0160"],"award-info":[{"award-number":["cstc2018jcyjAX0160"]}],"id":[{"id":"10.13039\/501100005230","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Educational Commission Foundation of Chongqing of China","award":["KJQN201900547, KJ120611"],"award-info":[{"award-number":["KJQN201900547, KJ120611"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Multi-focus image fusion is an important method used to combine the focused parts from source multi-focus images into a single full-focus image. Currently, to address the problem of multi-focus image fusion, the key is on how to accurately detect the focus regions, especially when the source images captured by cameras produce anisotropic blur and unregistration. This paper proposes a new multi-focus image fusion method based on the multi-scale decomposition of complementary information. Firstly, this method uses two groups of large-scale and small-scale decomposition schemes that are structurally complementary, to perform two-scale double-layer singular value decomposition of the image separately and obtain low-frequency and high-frequency components. Then, the low-frequency components are fused by a rule that integrates image local energy with edge energy. The high-frequency components are fused by the parameter-adaptive pulse-coupled neural network model (PA-PCNN), and according to the feature information contained in each decomposition layer of the high-frequency components, different detailed features are selected as the external stimulus input of the PA-PCNN. Finally, according to the two-scale decomposition of the source image that is structure complementary, and the fusion of high and low frequency components, two initial decision maps with complementary information are obtained. By refining the initial decision graph, the final fusion decision map is obtained to complete the image fusion. In addition, the proposed method is compared with 10 state-of-the-art approaches to verify its effectiveness. The experimental results show that the proposed method can more accurately distinguish the focused and non-focused areas in the case of image pre-registration and unregistration, and the subjective and objective evaluation indicators are slightly better than those of the existing methods.<\/jats:p>","DOI":"10.3390\/e23101362","type":"journal-article","created":{"date-parts":[[2021,10,20]],"date-time":"2021-10-20T01:23:46Z","timestamp":1634693026000},"page":"1362","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Multi-Focus Image Fusion Method Based on Multi-Scale Decomposition of Information Complementary"],"prefix":"10.3390","volume":"23","author":[{"given":"Hui","family":"Wan","sequence":"first","affiliation":[{"name":"College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"},{"name":"College of Computer and Information Science, Chongqing Normal University, Chongqing 401331, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xianlun","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiqin","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9033-8245","authenticated-orcid":false,"given":"Weisheng","family":"Li","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.inffus.2020.06.013","article-title":"Multi-focus image fusion: A Survey of the state of the art","volume":"64","author":"Yu","year":"2020","journal-title":"Inf. Fusion"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1109\/TIP.2020.3033158","article-title":"Global-feature Encoding U-Net (GEU-Net) for Multi-focus Image Fusion","volume":"30","author":"Bin","year":"2021","journal-title":"IEEE Trans. Image Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1109\/TIP.2004.823821","article-title":"Gradient-based multiresolution image fusion","volume":"13","author":"Petrovi","year":"2004","journal-title":"IEEE Trans. Image Process. Publ. IEEE Signal Process. Soc."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Liu, S., and Chen, J. (2016, January 13\u201316). A Fast Multi-Focus Image Fusion Algorithm by DWT and Focused Region Decision Map. Proceedings of the Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA), Jeju, Korea.","DOI":"10.1109\/APSIPA.2016.7820864"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1109\/TMM.2009.2017640","article-title":"Segmentation-driven image fusion based on alpha-stable modeling of wavelet coefficients","volume":"11","author":"Wan","year":"2009","journal-title":"IEEE Trans. Multimed."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.neucom.2015.10.084","article-title":"Hybrid dual-tree complex wavelet transform and support vector machine for digital multi-focus image fusion","volume":"182","author":"Yu","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"247","DOI":"10.18280\/ts.380201","article-title":"Multi-Focus Image Fusion with Multi-Scale Transform Optimized by Metaheuristic Algorithms","volume":"38","author":"Abas","year":"2021","journal-title":"Trait. Signal"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Li, Y., Sun, X., Huang, G., Qi, M., and Zheng, Z.Z. (2018). An image fusion method based on sparse representation and sum modified-laplacian in nsct domain. Entropy, 20.","DOI":"10.3390\/e20070522"},{"key":"ref_9","first-page":"210","article-title":"Multi-focus Image Fusion Method Based on Laplacian Eigenmaps Dimension Reduction in NSCT Domain","volume":"7","author":"Jia","year":"2021","journal-title":"Int. Core J. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2864","DOI":"10.1109\/TIP.2013.2244222","article-title":"Image fusion with guided filtering","volume":"22","author":"Li","year":"2013","journal-title":"IEEE Trans. Image Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1109\/TMM.2019.2928516","article-title":"Multi-Focus Image Fusion by Hessian Matrix based decomposition","volume":"22","author":"Xiao","year":"2020","journal-title":"IEEE Trans. Multimed."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"834","DOI":"10.1631\/FITEE.1900737","article-title":"Multi-focus image fusion based on fractional-order derivative and intuitionistic fuzzy sets","volume":"21","author":"Zhang","year":"2020","journal-title":"Front. Inf. Technol. Electron. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"479","DOI":"10.14429\/dsj.61.705","article-title":"Image fusion technique using multi-resolution singular value decomposition","volume":"61","author":"Naidu","year":"2011","journal-title":"Def. Sci. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"695960","DOI":"10.3389\/fnbot.2021.695960","article-title":"Multi-Focus Color Image Fusion Based on Quaternion Multi-Scale Singular Value Decomposition","volume":"15","author":"Wan","year":"2021","journal-title":"Front. Neurorobot."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1109\/LSP.2014.2354534","article-title":"Multi-focus image fusion based on spatial frequency in discrete cosine transform domain","volume":"22","author":"Cao","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s11045-015-0343-6","article-title":"Image fusion based on complex-shearlet domain with guided filtering","volume":"28","author":"Liu","year":"2017","journal-title":"Multidimens. Syst. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3367","DOI":"10.1109\/TIM.2018.2877285","article-title":"Image fusion using adjustable non-subsampled shearlet transform","volume":"68","author":"Vishwakarma","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1007\/s11760-018-1402-x","article-title":"Multi-focus image fusion with alternating guided filtering","volume":"13","author":"Zhang","year":"2019","journal-title":"Signal Image Video Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1117\/1.OE.54.12.123113","article-title":"Multifocus image fusion scheme based on the multiscale curvature in nonsubsampled contourlet transform domain","volume":"54","author":"Li","year":"2015","journal-title":"Opt. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Kou, L., Zhang, L., Zhang, K., Sun, J., Han, Q., and Jin, Z. (2018). A multi-focus image fusion method via region mosaic on laplacian pyramids. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0191085"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.inffus.2013.11.005","article-title":"Multi-scale weighted gradient-based fusion for multi-focus images","volume":"20","author":"Zhou","year":"2014","journal-title":"Inf. Fusion"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.neucom.2019.01.048","article-title":"Multi-focus image fusion using boosted random walks-based algorithm with two-scale focus maps","volume":"335","author":"Ma","year":"2019","journal-title":"Neurocomputing"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.neucom.2018.04.066","article-title":"A general memristor-based pulse coupled neural network with variable linking coefficient for multi-focus image fusion","volume":"308","author":"Dong","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.inffus.2021.06.008","article-title":"Image fusion meets deep learning: A survey and perspective","volume":"76","author":"Hao","year":"2021","journal-title":"Inf. Fusion"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1982","DOI":"10.1109\/TMM.2019.2895292","article-title":"FuseGAN: Learning to fuse multi-focus image via conditional generative adversarial network","volume":"21","author":"Guo","year":"2019","journal-title":"IEEE Trans. Multimed."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.ins.2018.03.040","article-title":"Quaternion polar harmonic Fourier moments for color images","volume":"450","author":"Wang","year":"2018","journal-title":"Inf. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1109\/TNN.2011.2128880","article-title":"A new automatic parameter setting method of a simplified PCNN for image segmentation","volume":"22","author":"Chen","year":"2011","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1109\/TIM.2018.2838778","article-title":"Medical image fusion with parameter-adaptive pulse coupled neural network in nonsubsampled shearlet transform domain","volume":"68","author":"Yin","year":"2019","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.inffus.2014.09.004","article-title":"A General Framework for Image Fusion Based on Multi-scale Transform and Sparse Representation","volume":"24","author":"Liu","year":"2015","journal-title":"Inf. Fusion"},{"key":"ref_30","unstructured":"Mostafa, A., Pardis, R., and Ali, A. (2017, January 22\u201323). Multi-Focus Image Fusion Using Singular Value Decomposition in DCT Domain. Proceedings of the 10th Iranian Conference on Machine Vision and Image Processing (MVIP), Isfahan, Iran."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.inffus.2011.07.001","article-title":"Image matting for fusion of multi-focus images in dynamic scenes","volume":"14","author":"Li","year":"2013","journal-title":"Inf. Fusion"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1334","DOI":"10.1016\/j.sigpro.2009.01.012","article-title":"Multifocus image fusion using the nonsubsampled contourlet transform","volume":"89","author":"Zhang","year":"2009","journal-title":"Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.inffus.2016.09.006","article-title":"Boundary finding based multi-focus image fusion through multi-scale morphological focus-measure","volume":"35","author":"Zhang","year":"2017","journal-title":"Inf. Fusion"},{"key":"ref_34","unstructured":"(2021, January 24). Available online: https:\/\/github.com\/sametaymaz\/Multi-focus-Image-Fusion-Dataset."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIM.2020.2991290","article-title":"A novel fast single image dehazing algorithm based on artificial multiexposure image fusion","volume":"70","author":"Zhu","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1007\/s10044-011-0235-9","article-title":"A classification and fuzzy-based approach for digital multi-focus image fusion","volume":"16","author":"Saeedi","year":"2013","journal-title":"Pattern Anal. Appl."},{"key":"ref_37","unstructured":"(2020, October 16). Available online: https:\/\/mansournejati.ece.iut.ac.ir\/content\/lytro-multi-focus-dataset."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/10\/1362\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:17:57Z","timestamp":1760167077000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/10\/1362"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,19]]},"references-count":37,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["e23101362"],"URL":"https:\/\/doi.org\/10.3390\/e23101362","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,19]]}}}